I like this comment from Pat:
In large measure men tend to be calculators. "What is in it for them". When they encounter someone the often think of what that person may be looking for. Women, on the other hand, tend to view things at multiple levels at the same time.
You as a TG women present an enigma to men. They do not get it, there is nothing that they want from you, they hope that there is nothing that you want from them and you can be a bit of a threat.
Women will not see you as a threat. You are interesting. You can interact with women on a woman to woman basis and you can bring along some of your 'guy' experiences.
I think that your analogy of changing teams is going in the right direction but perhaps it is more like changing sports. Sort of like going from playing for the Cincy Bengals and not finding yourself on the roster of the Cleveland Indians.
A good question becomes, "When do women see a transgender woman as a threat?" Over the years, on several discussion sites, I have seen this topic discussed. The most shallow response is always "a genetic woman may be threatened by a beautiful transgender woman's looks." While I agree a woman may feel a bit insecure when a former team player from the other side enters her world and competes "externally", very quickly the "multiple levels" Pat brought up kick in. No matter how "good" a cross dresser or transgender woman may look, another genetic woman will quickly discover how much of a woman they really are. From that point, a woman decides which "category" her new trans acquaintance fits in.
Of course the major threat of all to both genders is sex. Men are wrecked by us. I will add to Pat's observation "what if there is something a man wants from us?" At that point, the "gay" word is brought into the situation and confusion reigns. OMG could I be gay? - is what a man thinks when in fact "gay" is not a term which enters a true transgender woman's mind. I have had very limited sexual contact with men but when I did, I was doing it as a trans woman. I came away from the experiences wondering what the men thought of me as a woman.
At the least, the whole gender mix is a potent and interesting discussion topic. The sad part is seemingly the only non participants are the hardcore femme lesbians these days. It's no surprise though, a certain amount of the population can't grasp the idea of multiple genders and sexuality outside the binaries. It's complex!
In the meantime, as my genetic girlfriend told me last night, she really has very little idea of what makes men tick. She made the comment also "I should be the gender expert." I could only say, I'm amazed how little each gender knows about the other, when they are so transparent. It could be, Pat, calling transgender women and men "interesting" could be an understatement. "Mysterious" may be a better word!